We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.
翻译:我们提出一个假设测试,允许在混合板块线性回归模型中进行许多测试限制。 测试将常规F统计与一个关键值进行比较, 以纠正许多限制和有条件的四氯环乙烷性。 校正使用一输出估计来正确将关键值和三输出估计值集中到正确的尺度上。 测试的大型样本属性在一个无症状框架内确立, 测试限制的数量可以固定或随着样本大小的增长而增长, 甚至可以与观测数量成比例。 我们显示, 测试在微小样本中, 即使处于强度的六氯代苯性之下, 也具有与精确的F测试相同的本地替代物的非三氟性静态。 模拟证实了这些理论结论, 并提出了中等小样本的精细大小控制。